Symmetrize option doesn't mirror bones on the axis
Take a look at the following image.
The Arrows are pointing at the Object's Origin, if you move your objects (armatures too) in object mode, the Origin is going to be moved with the object. This origin is the way for Blender to &quot;say&quot; Here is the &quot;Left&quot; and here is the &quot;Right&quot;. So, you need to keep that origin in the center, also known as World Origin. If you wanna move an object, like your bones, switch to &quot;Edit Mode, select all the bones, and then move all bones to one side or the other.

Hope that helps.